Plz I need help! On these 3 questions!

An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.

we have that

5 miles -------> 10 minutes (direction of the wind)

5 miles ------> 1 hour (against the same wind)

therefore

10 miles ------> ? (without any wind)

so

Let

x -----> speed of the wind

y -----> speed of the airship

direction of the wind

speed=d/t ------> 5/10=0.5 miles per min

against the same wind

speed=5/60=1/12 miles per min

so

x+y=0.5 ------> x=0.5-y -----> equation 1

y-x=1/12 -----> equation 2

solve the system

substitute equation 1 in equation 2

y-(0.5-y)=1/12

2y=(1/12)+1/2

2y=7/12

y=7/24=0.2917 miles per min

Find the value of x

x=(1/2)-7/24

x=5/24=0.2083 miles per min

therefore

10 miles without any wind

speed=d/t ------> t=d/speed

t=10/(7/24)

The expression that represents the word phrase of the product of 3 and 6 more than a number is 3(6 + x).

Let the given number be x.

Therefore, the expression that represents the word phrase the product of 3 and 6 more than a number will be:

= 3(6 + x)

In conclusion, the correct option will be 3(6 + x).

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The probability for this event can be written (as a ratio, a decimal, and a percent) as:

Here we know that a number line contains 4 points, A, B, C, and D.

Such that:

A = 0

B = 10

C = 15

D = 18

We want to find the probability that a point chosen at random on AD is on BD

First, the distance AD is equal to:

AD = 18 - 0 = 18

The distance BD is:

BD = 18 - 10 = 8

The probability that a random point from AD also lies in BD is the quotient between the two lengths, then we will get:

P = 8/18 = 4/9

That is the ratio, and we can rewrite this as:

P = 4/9 = 0.44

And the percent form is that by 100%, so we get:

0.44*100% = 44%

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Answer: amount of variation

Step-by-step explanation:

The mean is a measure of the center whereas the standard deviation measures the variation of data about the mean.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
The mean is a measure of the center in the data set, whereas the standard deviation measures the variation of data about the mean in the data set.

Thus, the mean is a measure of the center whereas the standard deviation measures the variation of data about the mean.

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Answer:

- 7x + y = -30

2x - 5 = y

=> -7x + 2x - 5 = -30

2x - 5 = y

<=> -5x = -25

2x - 5 = y

<=> x = 5

y = 2.5 - 5 = 5

=> (x,y) = (5;5)

Answer:

y=7x-30

2x-5=7x-30

30-5=7x-2x

25=5x

x=5

if x = 5 substitute in any of the equations

y= 2*5 -5

y=5

According to initial condition, the correct option is: \(f(x) = ±4e^(18x^2)\)

Given : \(u dt du=e 2u+8t.\)

We need to solve the separable differential equation for the following initial condition \(u(0)=12\).

using integration of variable separable method \(u dt du=e 2u+8t\)

On Integrating both the sides, we get :

\(u^2 / 2 = (e 2u+8t) / 2 + c -------------(1)\)

Now, using the initial condition \(u(0)=12\), and putting it in equation:

\((1) 12^2 / 2 = (e^0) / 2 + c72 = 1 / 2 + c⇒ c = 143 / 2\)

Hence, the equation (1) becomes \(u^2 / 2 = (e 2u+8t) / 2 + 143 / 2\)

We need to find \(f(x) if y=f(x)\) satisfies \(dx dy=36yx 11\)and the y-intercept of the curve \(y=f(x) is 4.\)

using the variable separable method and integrating both sides , we get :

\(1 / y dy = 36x dx\)

on Integrating, we get:

\(ln|y| = 18x^2 + c ------(2)\)

using the y-intercept condition, we get :

\(ln|4| = 18 (0)^2 + c ln|4| = c\)

putting this value of c in the equation (2) we get:

\(ln|y| = 18x^2 + ln|4|ln|y| = ln|4| + 18x^2\)

Taking exponent on both sides, we get:

\(|y| = 4 e^(18x^2)\)

Now, the y-coordinate can be positive or negative.

So, we will take

\(y = + 4 e^(18x^2) and y = - 4 e^(18x^2)\)

So, \(f(x) = + 4 e^(18x^2) or f(x) = - 4 e^(18x^2)\)

The correct option is: \(f(x) = ±4e^(18x^2).\)

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The function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

To find f(t) from the Laplace transform ℋ(f(t)), we need to apply the inverse Laplace transform ℒ⁻¹ to ℋ(f(t)).

Given ℋ(f(t)) = ℋ{s(t)}, we have:

ℒ⁻¹{ℋ(s(t))} = ℒ⁻¹{ℋ[(s + 1)²/s]} = ℒ⁻¹{ℋ[s/s] + ℋ[2s/(s+1)²] + ℋ[1/(s+1)²]}

Using the properties of Laplace transforms and taking the inverse Laplace transforms, we get:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

where u(t) is the unit step function.

Therefore, the function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

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Answer:

a. Income = $408.75

b. Income = $300 + $0.05x

Step-by-step explanation:

Given

Salary = $300 weekly

Commission = 5% of total sales

Solving (a): When total sales = $2175

To calculate his total income, we make use of...

Income = Salary + 5% * Total Sales

\(Income = \$300 + 5\% * \$2175\)

\(Income = \$300 + \$108.75\)

\(Income = \$408.75\)

Solving (b): When total sales = $x

Income = Salary + 5% * Total Sales

\(Income = \$300 + 5\% * \$x\)

Convert % to decimal

\(Income = \$300 + 0.05 * \$x\)

\(Income = \$300 + \$0.05x\)

ANSWER

x＝24

Step-by-step explanation:

x＋180＋156＝360

180＋156＝336

x＋336＝360

x＝360-336

x＝24

The objective function represents the mathematical expression that the model seeks to optimize. In this case, the expression is x 2y -z2. This means that the model is trying to find the combination of values for x, y, and z that maximize this expression.

To determine which of the following statements is true, we need to analyze the given objective function formula x 2y -z2 in relation to the decision variables x, y, and z.

The objective function represents the mathematical expression that the model seeks to optimize. In this case, the expression is x 2y -z2. This means that the model is trying to find the combination of values for x, y, and z that maximize this expression.

To do this, the model may have certain constraints or limitations that need to be taken into account. These constraints can be represented as inequalities or equations involving the decision variables.

Without any additional information about the model's constraints, it is difficult to determine which of the following statements is true. The statements could be related to the feasibility of the model's solutions, the optimal values of the decision variables, or the sensitivity of the objective function to changes in the decision variables.

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Answer:

66 years

Step-by-step explanation:

1) Convert 1.4426 * 10^4 into a number....

     = 14426

2) Divide

14426 / 218.58  

= 65.9987190045

About 66 years

That's all you write cause they asked u in years, no month or other stuff :)

Answer:

Approximately 66 years

Step-by-step explanation:

1.4426×\(10^{4}\) mm is equal to 14,426mm

14,426mm÷218.58=65.998...≅66

A sample size of at least 61 salmon should be taken to estimate the mean weight of salmon caught by a fishing company with a margin of error of ±2 lb and a confidence level of 90%.

To determine the sample size required to estimate the mean weight of salmon caught by a fishing company with a 90% confidence interval and a margin of error of ±2 lb, we can use the formula:

n = (z^2 * σ^2) / E^2

where n is the sample size, z is the z-score for the desired confidence level (in this case, 1.645 for 90% confidence), σ is the standard deviation of the population (5.5 lb), and E is the desired margin of error (2 lb).

Substituting these values into the formula, we get:

n = (1.645^2 * 5.5^2) / 2^2

n = 60.16

Rounding up to the nearest whole number, we need a sample size of at least 61 salmon to be 90% confident that our point estimate of the mean weight is within ±2 lb of the true mean weight.

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Answer:

yes I can help you with this but I don't know it

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoint of the segment CD is given as C(-2, -4) and D(6, 2). Then the mid-point of the line segment CD will be

(x, y) = [(-2 + 6) / 2, (-4 + 2) / 2]

(x, y) = (4/2, -2/2)

(x, y) = (2, -1)

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

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Answer:

1/3^4

1/81

Step-by-step explanation:

(3^2)^-2

We know that a^b^c = a^(b*c)

3 ^(2*-2)

3^-4

We know that a^-b = 1/a^b

1/3^4

1/81

Answer:

Thanks for the points... dude.....

In this scenario, the domain would be the set of all possible values for the amount of time it takes Sammy Speedster to drive from Houston to San Antonio. Since he is driving on a daily basis, the domain could be considered a continuous range from zero to some maximum value, perhaps 10 hours.

It's possible that Sammy could complete the trip in less than 3 hours if he were driving at a very high speed, but this would not be a common occurrence. Therefore, a reasonable domain could be considered to be between 3 and 10 hours.

The range, on the other hand, would be the set of all possible distances that Sammy could drive in the allotted time. Since we know that the distance is a constant 200 miles, the range would simply be 200 miles. It's possible that Sammy could drive more than 200 miles in a day if he were assigned additional routes, but this would not be relevant to this scenario.

In summary, a reasonable domain for Sammy's logbook would be between 3 and 10 hours, and the range would be a constant 200 miles.

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In a four-candidate race with 107 votes cast, the smallest number of votes a winning candidate can have is 28.

In a four-candidate race decided by plurality, the winning candidate is the one who receives the most votes, regardless of whether that number of votes constitutes a majority (more than 50%) of the total votes cast.

To determine the smallest number of votes a winning candidate can have in a four-candidate race with 107 votes cast, we can assume that the other three candidates each receive an equal number of votes, say x. Then, the winning candidate must receive more votes than each of the other three candidates.

So, the minimum number of votes the winning candidate can receive is x + 1.

The total number of votes cast in the election is:

x + x + x + (x + 1) = 4x + 1

Since we know that 4x + 1 = 107, we can solve for x:

4x + 1 = 107

4x = 106

x = 26.5

Since x must be a whole number, we can round up to x = 27.

Then, the minimum number of votes the winning candidate can have is:

27 + 1 = 28

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After the measurement of the worm and after conclusion of their measurement it cannot be said that the worms are of equal length and the maximum possible difference between the length of the two worms can be 0.8 cm.

Adra and Leila measured two different worms and they concluded that their worms were about 11 cm long. Both of them rounded off their measurements. Rounding off of numbers means making the number equal to the nearest whole number possible. If we assume that measurement of Adra's worm gave the number 10.6 cm, then the nearest whole number to 10.6 cm is 11 cm and if we assume that measurement of Leila's worm gave the number 11.4 cm then also the nearest whole number is 11 cm. This proves that both the worms were not of same size. Now, the maximum possible difference between the length of the two worms can be 11.4 - 10.6 = 0.8 cm.

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After  solving the equation 5(X - C)  = D , for the given matrices , we get , the unknown matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

In the question ,

it is given that , the matrices are

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) .

and the equation is given as 5(X - C)  = D ,

and we have to find the value of unknown matrix X .

let the matrix X be = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\)

Substituting , the given matrices A , B , C and D in the equation 5(X - C)  = D ,

we get ,

5(X - C)  = D ,

5X - 5C = D ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) - 5\(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\)

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) - \(\left[\begin{array}{ccc}15&15\\20&0\\0&40\end{array}\right]\)

Simplifying further ,

we get ,

5\(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}25&45\\50&30\\30&40\end{array}\right]\)

Dividing both sides by 5 ,

we get ,

X = \(\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right]\) = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\)

Therefore , the matrix X is = \(\left[\begin{array}{ccc}5&9\\10&6\\6&8\end{array}\right]\) .

The given question is incomplete , the complete question is

Solve the matrix equation for the unknown matrix X.

A = \(\left[\begin{array}{ccc}7&3\\4&3\end{array}\right]\)   B = \(\left[\begin{array}{ccc}7&2\\7&2\end{array}\right]\)   C = \(\left[\begin{array}{ccc}3&3\\4&0\\0&8\end{array}\right]\)   and D = \(\left[\begin{array}{ccc}10&30\\30&30\\30&0\end{array}\right]\) . the equation is

5(X - C)  = D .

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Answer:

1. 453

2. 39.5

Step-by-step explanation:

Answer:

8 I think

Step-by-step explanation:

Answer:

Locke, Rousseau and Montesquieu agreed that nations would be built on social institutions, or even what Montesquieu considered a legislation which would describe the laws of the country and put in concrete what privileges the citizens and the state have.

Answer:

d 18,328

Step-by-step explanation:

I did the math >:3

sorry if it's wrong

Answer:

4 1/8

Step-by-step explanation:

subtracting a whole number with a fraction just means I have to change one of the numbers so they match with the other.

meaning I should change the whole number 5 to a fraction.

I will use the bottom number to figure out what the fraction in the whole number should look like.

5 = 5/1

I want the bottom number to be 8 like the other fraction 7/8

I multiply the top and bottom number of 5/1 by 8, giving me

40/8

now I subtract 40/8-7/8 = 33/8 or 4 and 1/8

Answer: 1.4 days

Step-by-step explanation:

Part A: The likelihood that a chosen egg will hatch in less than 18 days:

Part B: The likelihood chosen egg longer than 20 days; 15.87%.

You can apply the z-test since you are aware of the population standard deviation and that the population has a normal distribution.

Part A: The likelihood that a randomly chosen egg will hatch in less than 18 days:

Create your test statistic by using:

P(< 18 days)

z< (x-μ)/σ

z < (18-19)/1

z<-1

This equates to p = 0.1587 to use a probability table (note that this is one-sided).

Part B:  The likelihood that a randomly chosen egg would take longer than 20 days to hatch;

Develop your test statistic by:

P(> 20 days)

z > (20-19)/1

z<1

This equates to p = 0.1587 to use a probability table (note that this is one-sided).

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The correct question is-

The mean incubation time for a type of fertilized egg is 19 days.  Suppose the incubation times are approximately normally distrubuted with a standard deviation of 1 day.

A. What is the probability a randoly selected egg hatches in less than 18 days

B. What is the probability a randomly selected egg hatches takes over 20 days

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

Using proportions, it is found that the correct statement is:

D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.

A proportion is a fraction of a total amount.

In this problem, the table is from a sample of 80 visitors.

Since the proportions stay the same, just the number of visitors change, the correct statement is given by:

D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports.

As from the 80 students, 28 prefer camping and 14 prefer water sports, hence from 200, these numbers will be of 70 and 35 respectively.

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Answer: D. The number of visitors who prefer camping will be 2 times the number of visitors who prefer water sports

Step-by-step explanation: If you add up all the number of visitors, you'll get 80. Since we want to find the numbers for the next 200 visitors, we'll divide 200 by 80, which will get us 2.5. Then you'll multiply all the numbers by 2.5 to get:

Camping = 70

Hiking Trails = 55

Water Sports = 35

Biking Trails = 40

After that, you'll just compare the numbers to get your answer.    

Answer:

A. 5 ¼ miles

Step-by-step explanation:

t = time

d = distance

15 min. = ¼ hour

1 ½ hr – ¼ hr ≤ t ≤ 1 ½ hr + ¼ hr (subtract & add fractions)

           1 ¼ hr ≤ t ≤ 1 ¾ hr

If   t = 1 ¼ hour

Then     d = 3 miles/hr * 1 ¼ hr (cross hours & multiply)

              d = 3 ¼ miles

If   t = 1 ¾  hour

Then     d = 3 miles/hr * 1 ¾  hr (cross hours & multiply)

              d = 5 ¼ miles

Hope this help! :)